# Normal

#### Description This sketch allows you to change the parameters of a normal curve and compute the area under any portion of it. The formula for the normal curve is shown above. There are three parameters to change, each corresponding to a point in the sketch.

• The parameter A controls the maximum height of the curve, which is . You can drag the point at the top of the curve to change its height.
• The mean (μ in the formula) is controlled by the point labeled mean in the sketch.
• The standard deviation is σ.

Press Show Integral to get two control points, xi and xf. The area under the curve between these two values will be shown in pink and computed numerically.

#### Questions

1. Demonstrate the assertion that about two-thirds of the area under a normal curve lies within plus or minus one standard deviation of the mean.
2. Use the sketch to find the proportion of the area under the curve that lies to the right of the mean plus one standard deviation.
3. Lengths of tadpoles in a certain pond are found to be approximately normally distributed with a mean of 1.25 inches and a standard deviation of .25 inches. Use the sketch to find the chances of finding a tadpole with a length greater than 1.75 inches.